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GMSK
In digital modulation, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying that was developed in the late 1950s by Collins Radio employees Melvin L. Doelz and Earl T. Heald. Similar to OQPSK, MSK is encoded with bits alternating between quadrature components, with the Q component delayed by half the symbol period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion. In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous-phase frequency-shift keyed (CPFSK) signal with a frequency separation of one-half the bit rate. In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation is w ...
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GMSK PSD
In digital modulation, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying that was developed in the late 1950s by Collins Radio employees Melvin L. Doelz and Earl T. Heald. Similar to OQPSK, MSK is encoded with bits alternating between quadrature components, with the Q component delayed by half the symbol period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion. In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous-phase frequency-shift keyed (CPFSK) signal with a frequency separation of one-half the bit rate. In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation ...
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Gaussian Minimum-shift Keying
In digital modulation, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying that was developed in the late 1950s by Collins Radio employees Melvin L. Doelz and Earl T. Heald. Similar to OQPSK, MSK is encoded with bits alternating between quadrature components, with the Q component delayed by half the symbol period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion. In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous-phase frequency-shift keyed (CPFSK) signal with a frequency separation of one-half the bit rate. In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation is ...
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Digital Modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the '' carrier signal'', with a separate signal called the ''modulation signal'' that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer. The carrier is higher in frequency than the modulation signal. In radio communication the modulated carrier is transmitted through space as a radio wave to a radio receiver. Another purpose is to transmit multiple channels of information through a single communication medium, using frequency-division multiplexing (FDM). For example in cable television which uses FDM, many carrier signals, each modulated with a different television channel, are transported thro ...
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Gaussian Filter
In electronics and signal processing mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would have infinite impulse response). Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. A Gaussian filter will have the best combination of suppression of high frequencies while also minimizing spatial spread, being the critical point of the uncertainty principle. These properties are important in areas such as oscilloscopes and digital telecommunication systems. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. Definition The one-dimensional Gaussian filter has an im ...
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CPFSK
Continuous phase modulation (CPM) is a method for modulation of data commonly used in wireless modems. In contrast to other coherent digital phase modulation techniques where the carrier phase abruptly resets to zero at the start of every symbol (e.g. M- PSK), with CPM the carrier phase is modulated in a continuous manner. For instance, with QPSK the carrier instantaneously jumps from a sine to a cosine (i.e. a 90 degree phase shift) whenever one of the two message bits of the current symbol differs from the two message bits of the previous symbol. This discontinuity requires a relatively large percentage of the power to occur outside of the intended band (e.g., high fractional out-of-band power), leading to poor spectral efficiency. Furthermore, CPM is typically implemented as a constant-envelope waveform, i.e., the transmitted carrier power is constant. Therefore, CPM is attractive because the phase continuity yields high spectral efficiency, and the constant envelope yields exce ...
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Frequency-shift Keying
Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier signal. The technology is used for communication systems such as telemetry, weather balloon radiosondes, caller ID, garage door openers, and low frequency radio transmission in the VLF and ELF bands. The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the 1 is called the mark frequency and the 0 is called the space frequency. Modulating and demodulating Reference implementations of FSK modems exist and are documented in detail. The demodulation of a binary FSK signal can be done using the Goertzel algorithm very efficiently, even on low-power microcontrollers. Variations Multiple frequency-shift keying Continuous-phase frequency-shift keying In principle FSK can be implemented by using completely independent free-running ...
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Continuous Phase Modulation
Continuous phase modulation (CPM) is a method for modulation of data commonly used in wireless modems. In contrast to other coherent digital phase modulation techniques where the carrier phase abruptly resets to zero at the start of every symbol (e.g. M- PSK), with CPM the carrier phase is modulated in a continuous manner. For instance, with QPSK the carrier instantaneously jumps from a sine to a cosine (i.e. a 90 degree phase shift) whenever one of the two message bits of the current symbol differs from the two message bits of the previous symbol. This discontinuity requires a relatively large percentage of the power to occur outside of the intended band (e.g., high fractional out-of-band power), leading to poor spectral efficiency. Furthermore, CPM is typically implemented as a constant-envelope waveform, i.e., the transmitted carrier power is constant. Therefore, CPM is attractive because the phase continuity yields high spectral efficiency, and the constant envelope yields exce ...
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QPSK
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a precise time. It is widely used for wireless LANs, RFID and Bluetooth communication. Any digital modulation scheme uses a finite number of distinct signals to represent digital data. PSK uses a finite number of phases, each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal such a system is ...
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Electrical Power
Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively. A common misconception is that electric power is bought and sold, but actually electrical energy is bought and sold. For example, electricity is sold to consumers in kilowatt-hours (kilowatts multiplied by hours), because energy is power multiplied by time. Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electrical grid. Electric power can be delivered over long distances by transmission lines and used for applications such as motion, light or heat with high effi ...
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Spectral Efficiency
Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is utilized by the physical layer protocol, and sometimes by the medium access control (the channel access protocol). Guowang Miao, Jens Zander, Ki Won Sung, and Ben Slimane, Fundamentals of Mobile Data Networks, Cambridge University Press, , 2016. Link spectral efficiency The link spectral efficiency of a digital communication system is measured in ''bit/ s/ Hz'', or, less frequently but unambiguously, in ''(bit/s)/Hz''. It is the net bit rate (useful information rate excluding error-correcting codes) or maximum throughput divided by the bandwidth in hertz of a communication channel or a data link. Alternatively, the spectral efficiency may be measured in ''bit/symbol'', which is equivalent to ''bits per channel use'' (''bpcu''), implying tha ...
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Q-function
In statistics, the Q-function is the tail distribution function of the standard normal distribution. y) = P(X > x) = Q(x) where x = \frac. Other definitions of the ''Q''-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally. Because of its relation to the cumulative distribution function of the normal distribution, the ''Q''-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics. Definition and basic properties Formally, the ''Q''-function is defined as :Q(x) = \frac \int_x^\infty \exp\left(-\frac\right) \, du. Thus, :Q(x) = 1 - Q(-x) = 1 - \Phi(x)\,\!, where \Phi(x) is the cumulative distribution function of the standard normal Gaussian distribution. The ''Q''-function can be expressed in terms of the error function, or the complementary error function, as : \begin Q(x) &=\frac\left( \frac \int_^\infty \exp\left(-t^2\right) ...
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Adaptive Equalizer
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading. Adaptive equalizers are a subclass of adaptive filters. The central idea is altering the filter's coefficients to optimize a filter characteristic. For example, in case of linear discrete-time filters, the following equation can be used: : \mathbf_ = \mathbf^\mathbf where \mathbf_ is the vector of the filter's coefficients, \mathbf is the received signal covariance matrix and \mathbf is the cross-correlation vector between the tap-input vector and the desired response. In practice, the last quantities are not known and, if necessary, must be estimated during the equalization procedure either explicitly or implicitly. Many adaptation strategies exist. They include, e.g.: * Least mean squares filter (LMS) Note th ...
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